From what I know, most banking applications periodically store the account balance at a certain point in time as it would not be plausible to calculate it over the entire history of transactions every time it is needed. In order to find the account balance, the application would first load the latest balance saved and add transactions that occurred after that point.
What is this process of saving account balances called? What are some common techniques used in this process?(e.g., run it on every weekend night)
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While not specific to the banking industry I would call the technical process snapshotting.
When and how you should take your snapshots is going to vary based on your domain and specific requirements. The main reason to take a snapshot is performance (as you mentioned it saves you from having to go through the entire line of events that brought you to the current point). There is also a performance cost in generating and saving that snapshot. Ideally you should take your snapshots right at the point where the performance cost of taking a snapshot is less than the performance cost of going through the entire chain of events.